1. Install Dropbox (I used version 1.0.10)
2. Choose preferences and uncheck “Show desktop notifications” and “Start Dropbox on system startup”
3. Exit Dropbox by clicking exit in the context menu that shows when right clicking icon in task bar
4. Execute at command line prompt:

Make sure that you go into the Control Panel and use
the Services applet to change the Account Name and
Password that this newly installed service will use
for its Security Context.

Next is to change the user for witch the newly added service “Dropbox” runs under. Change this to Administrator.
5. Choose properties on Dropbox service.
6. Click on tab “Log On”
7. Click “This account”, and select Admimistrator. Set appropriate password.
8. Click Apply and OK

If this is the first time you have done this procedure for the administrator user, you will get an notification saying that the “Administrator user has been granted log on as service rights”

Next is to setup some registry settings for the service
9. Start > Run > regedit
10. Navigate to HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Dropbox
11. Create a new key “Parameters”
12. Add a new string value “Application”, (type REG_SZ). Set the value to the path to the dropbox.exe binary. Find the location by right clicking on the Dropbox icon on the desktop. Simply copy the path from there.
13. Close Registry Editor
14. Go back to Services, and start the Dropbox service

Now everything should be in place and work correctly.

Addition: It works fine to stop the Dropbox service, then start Dropbox and make changes in preferences etc, save changes and exit Dropbox. Then you can start Dropbox service again without problems. Work very neat actually. Running now on Windows Server 2003 and Windows Server 2008 64-bit. On Windows Server 2008 you can just copy instsrv.exe and srvany.exe to a folder under Program Files and create the Dropbox service from there.